Estimation of conditional quantiles from data with additional measurement errors.

Abstract Motivated by an application in the context of experimental fatigue tests we study the problem of estimating conditional quantiles from data that contains additional measurement errors. The only assumption on these errors is that a weighted sum of the absolute errors tends to zero with probability one for sample size tending to infinity. We show that the plug-in quantile estimate corresponding to a local averaging estimate of the conditional distribution function (codf) approaches the quantile set asymptotically, presumed that the local averaging estimate of the codf is pointwise strongly consistent. We also investigate the rate of convergence and show that our plug-in estimate achieves at least the same pointwise rate of convergence as the local averaging estimate of the codf plus the square root of the weighted sum of the absolute errors. Finally, the results are applied in simulations and in the context of experimental fatigue tests. Highlights • Nonparametric quantile estimation of number of cycles in experimental fatigue tests. • Consistency result for quantile estimate based on data with measurement errors (ME). • Proof of rate of convergence for this quantile estimate based on data with ME. [ABSTRACT FROM AUTHOR]